One is a process the other is a feeling.

in philosophy, analytical philosophy focuses on the strict application of logic in order to determine the veracity or otherwise or paradox of a proposition. So in philosophical terms they amount to the same thing.

In logical thinking, you proceed through the logical steps 1, 2, 3 . . .

In analytical thinking, you analyze each element of the situation before proceeding.

You can be one without the other. Being over analytical is illogical. It’s a great to get the balance right. I second what @marinelife said.

In my mind, it is helpful to employ both methods and I do differentiate them as follows: when you employ logical thinking, you draw conclusions from events previous to events future without extraneous points – when you employ analytical thinking, you begin to explain how any of the points got to the others. Basically, logical is Watson, analytical is Holmes.

Deductive logic argues from specific points to general conclusions.
Inductive logic argues from a general case to a specific instance.

Analytical thinking breaks complex phenomena into simpler, identifiable components to facilitate more careful examination and testing. Operational definitions are very important in specifying components to be tested scientifically.

I think it’s the other way around, @Dr_Lawrence: inductive reasoning proceeds from the particular to the general, and deductive from the general to the particular. The classic illustration of deductive reasoning is this:

1. All men are mortal
2. Socrates is a man
3. Therefore, Socrates is mortal

That major premise (1) is a generality from which, given the minor premise (2), the conclusion (3) necessarily follows.

Nicely made distinction in answer to the OP’s question.